Diversity of exact solutions and solitary waves with the influence of damping effect in ferrites materials

2022 ◽  
pp. 168995
Author(s):  
Usman Younas ◽  
Muhammad Bilal ◽  
Jingli Ren
Keyword(s):  
Exact Solutions ◽  
Solitary Waves ◽  
Damping Effect

EXACT SOLUTIONS AND COMPLEX WAVE EXCITATIONS OF GENERALIZED SASA–SATSUMA SYSTEM IN (2+1)-DIMENSIONS

2009 ◽  
Vol 23 (19) ◽  
pp. 3931-3938 ◽  
Author(s):  
CHUN-LONG ZHENG ◽  
JIAN-FENG YE
Keyword(s):  
Exact Solutions ◽  
Solitary Waves ◽  
Bäcklund Transformation ◽  
Periodic Wave ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Complex Wave

Starting from a Painlevé–Bäcklund transformation, an exact variable separation solution with four arbitrary functions for the (2+1)-dimensional generalized Sasa–Satsuma (GSS) system are derived. Based on the derived exact solutions in the paper, some complex wave excitations in the (2+1)-dimensional GSS system and revealed, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave background are also briefly discussed.

BIFURCATION, EXACT SOLUTIONS AND NONSMOOTH BEHAVIOR OF SOLITARY WAVES IN THE GENERALIZED NONLINEAR SCHRÖDINGER EQUATION

2005 ◽  
Vol 15 (10) ◽  
pp. 3295-3305 ◽  
Author(s):  
WEI WANG ◽  
JIANHUA SUN ◽  
GUANRONG CHEN
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Heteroclinic Orbits ◽  
Nonlinear Schrödinger ◽  
Generalized Nonlinear Schrödinger Equation ◽  
Planar Dynamical Systems

In this paper, the generalized nonlinear Schrödinger equation (GNLS) is studied. The bifurcation of solitary waves of the equation is discussed first, by using the bifurcation theory of planar dynamical systems. Then, the respective numbers of solitary waves are derived under different conditions on the equation parameters. Exact solutions of smooth solitary waves are obtained in the explicit form of a(ξ)ei(ψ(ξ)-ωt), ξ = x - vt by qualitatively seeking the homoclinic and heteroclinic orbits for a class of Liénard equations. Finally, nonsmooth solitary wave solutions of the GNLS are investigated.

scholarly journals Solitary-Wave and Periodic Solutions of the Kuramoto-Velarde Dispersive Equation

2016 ◽  
Vol 46 (3) ◽  
pp. 65-74 ◽  
Author(s):  
Ognyan Y. Kamenov
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Solitary Waves ◽  
Transformation Method ◽  
Dispersive Equation ◽  
Bilinear Transformation ◽  
Mapping Approach ◽  
Solitary Solutions

Abstract In the present paper, solitary solutions of the Kuramoto- Velarde (K-V) dispersive equation have been found, using the deformation and mapping approach. These exact solutions show the dynamics and the evolution of dispersive solitary waves. In the case α2 = α3, three families of exact periodic solutions have been obtained by employing the bilinear transformation method.

scholarly journals Conservation laws and exact solutions for the generalized Ostrovsky equation using symmetry analysis

2021 ◽  
Author(s):  
Sol Sáez
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Symmetry Analysis ◽  
Partial Differential ◽  
Wide Range ◽  
Depth Study ◽  
Ostrovsky Equation

In this work we consider a generalized Ostrovsky equation depending on two arbitrary functions and we make an in-depth study of this equation. We obtain the Lie symmetries which are admitted by this equation and some exact solutions as a periodic or solitary waves, obtained through ordinary and partial differential equations. Also, by means of the concept of multiplier, we obtain a wide range of conservation laws which preserve properties of the generalized Ostrovsky equation.

New Exact Solutions and Interactions Between Two Solitary Waves for (3+1)-Dimensional Jimbo–Miwa System

2008 ◽  
Vol 49 (5) ◽  
pp. 1245-1248 ◽  
Author(s):  
Ma Song-Hua ◽  
Fang Jian-Ping ◽  
Hong Bi-Hai ◽  
Zheng Chun-Long
Keyword(s):  
Exact Solutions ◽  
Solitary Waves ◽  
New Exact Solutions

scholarly journals New Exact Solutions of the Generalized Benjamin–Bona–Mahony Equation

Symmetry ◽  
2018 ◽  
Vol 11 (1) ◽  
pp. 20 ◽  
Author(s):  
Behzad Ghanbari ◽  
Dumitru Baleanu ◽  
Maysaa Al Qurashi
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Solitary Waves ◽  
Function Method ◽  
Optical Solitons ◽  
Nonlinear Pdes ◽  
Symbolic Computations ◽  
New Exact Solutions ◽  
Physical Features ◽  
Maple Package

The recently introduced technique, namely the generalized exponential rational function method, is applied to acquire some new exact optical solitons for the generalized Benjamin–Bona–Mahony (GBBM) equation. Appropriately, we obtain many families of solutions for the considered equation. To better understand of the physical features of solutions, some physical interpretations of solutions are also included. We examined the symmetries of obtained solitary waves solutions through figures. It is concluded that our approach is very efficient and powerful for integrating different nonlinear pdes. All symbolic computations are performed in Maple package.

A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws

2021 ◽  
Vol 143 ◽  
pp. 110486
Author(s):  
Nisa Çelik ◽  
Aly R. Seadawy ◽  
Yeşim Sağlam Özkan ◽  
Emrullah Yaşar
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Nonlinear Elastic
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